New research from Moneyfacts this week underlined just how bad things have got for savers in recent years. It shows that in order to earn just £100 interest annually before tax, you would have to have more than £11,000 saved in a typical no-notice account. But there are still some good deals around – this week, an instant access account paying 2.65% was launched.

Savings rates will be in the spotlight again next week when the Bank of England announces its base rate decision amid talk about a possible further reduction.

Moneyfacts says that last month, the average no-notice savings account offered 0.9% interest, while a typical notice account paid 1.17%. Five years ago the equivalent figures were 4.08% and 4.23%.

That means that to get the same £100 return on your savings cash as five years ago, you would need to put an additional £8,660 into an instant access account, says the data provider. "This highlights the heartbreak currently facing pensioners trying to supplement incomes, and also potential first-time buyers who are desperately trying to save for deposits," it adds.

There are some accounts paying half-decent rates available if you look hard enough. This week, Leeds building society launched Bonus Access Saver, paying 2.65% gross, which it said was "the top paying account available on the high street with instant access".

Bonus Access Saver pays a variable 2.05%, boosted by a bonus of 0.6% until 30 September 2013. The minimum investment is £100, with a maximum investment of £20,000 (£40,000 for joint accounts). Unlimited withdrawals can be made at any time, while additional payments in can be made while the account is open to new customers.

The Leeds this week also launched its Bonus Isa, which has a headline tax-free rate of 3%. It is aimed at those who haven't yet used their 2012-13 Isa allowance of £5,640. The account's interest rate is 1.3%, plus a 1.7% bonus until 30 September 2013, and the minimum investment is £1. During the bonus period, two withdrawals or transfers can be made without notice or loss of interest, and from 1 October 2013 there are no restrictions on withdrawals. However, transfers in of previous years' Isa subscriptions are not allowed.

In other savings news, Nationwide building society has reduced the rate and bonus on its MySave Online Plus account to 2.86% monthly (2.9% AER), which includes a 1.36% bonus for 12 months. However, it remains in the top 10 comparable accounts with a bonus, said Moneyfacts. The account can be opened with £1,000-plus. Only one free withdrawal is allowed per year.

Meanwhile, Derbyshire building society replaced its NetSaver with a new version paying a lower rate and bonus. Issue 5 pays 2.9% yearly; this includes a 1.9% bonus until 31 January 2014. The account is available to those over 16 with £1,000 or more to hand.